The Other Russia opposition coalition announced its plans for the assembly, which they hope will unite varying anti-Kremlin groups, in mid-March.
The charter read that while the assembly recognized that many of its members had "different, at times contradictory, views on many issues," its participants would "follow common principles allowing us to jointly struggle for the preservation of the unity of the people and a restoration of a just rule of a peaceful society in our country."
The Other Russia movement has said that 700 delegates from 66 Russian regions, representing 85 public and political groups, are involved in the assembly.
Leading figures in the Other Russian movement include Garry Kasparov, the former world chess champion, and Eduard Limonov, the writer and leader of the banned National Bolshevik Party.
Kasparov said on Saturday that the national assembly was the "only way to ensure a future for our country," adding that any attempt to change political reality always begins when "people are ready to reach an agreement with one another."
Limonov called for branches of the alternative parliament to be set up all over Russia.
Moscow police detained 14 members of the youth movement 'Molodaya Gvardiya' as they held an unsanctioned rally outside the building where the first meeting of the alternative parliament was taking place.
Some 20 members of the movement held signs reading, "No one elected you!" and "The National Assembly - the same faces with a different flag."
Russian pposition groups called the March 2 polls that brought Dmitry Medvedev to power "undemocratic" and "a farce," citing among other complaints the refusal of electoral authorities to register a number of candidates, including the former Russian prime minister, Mikhail Kasyanov.
The opposition also complained of unequal access to the media and the use of administrative resources to back Medvedev, who received just over 70% of the vote.